Question: Simplify the expression. $(-5x^{4}+3x^{2})(-4x^{4}-4x^{3}+6x^{2})$
Solution: First use the distributive property. $ - 5 x^4 (-4 x^4) - 5 x^4 (-4 x^3) - 5 x^4 (6 x^2) + 3 x^2 (-4 x^4) + 3 x^2 (-4 x^3) + 3 x^2 (6 x^2) $ Simplify. $ 20x^{8} + 20x^{7} - 30x^{6} - 12x^{6} - 12x^{5} + 18x^{4} $ $20x^{8}+20x^{7}-42x^{6}-12x^{5}+18x^{4}$ Identify like terms. $ { 20x^{8}} {+ 20x^{7}} {- 30x^{6}} {- 12x^{6}} {- 12x^{5}} {+ 18x^{4}} $ Add the coefficients. $ { 20x^{8}} {+ 20x^{7}} { -42x^{6}} { -12x^{5}} {+ 18x^{4}} $